Subgroups — C₁₃₇×#28640 #46878026

Order 35072.

854 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2567×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2548×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2065×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1987×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1982×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1934×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	C₄×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#124×C₁₃₇	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	#486×C₁₃₇	—	2	4	no	—
15	C₈×Q₈×C₁₃₇	—	2	4	no	—
16	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	#395×C₁₃₇	—	2	2	no	—
25	#394×C₁₃₇	—	2	2	no	—
26	#391×C₁₃₇	—	2	1	no	—
27	#390×C₁₃₇	—	2	1	no	—
28	#390×C₁₃₇	C₂²	1	4	yes	—
29	#389×C₁₃₇	C₂²	1	4	yes	—
30	#384×C₁₃₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	#340×C₁₃₇	C₂²	1	2	yes	—
34	#340×C₁₃₇	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₃₇	—	2	1	no	—
36	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₃₇	—	2	1	no	—
38	C₂²×D₄×C₁₃₇	—	2	1	no	—
39	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
44	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
45	#127×C₁₃₇	—	2	2	no	—
46	#127×C₁₃₇	—	2	2	no	—
47	#124×C₁₃₇	—	4	4	no	—
48	C₄×Q₈×C₁₃₇	—	2	2	no	—
49	C₄×Q₈×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
59	C₂×C₄²×C₁₃₇	—	2	1	no	—
60	C₂×C₄²×C₁₃₇	—	2	1	no	—
61	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
63	#106×C₁₃₇	—	2	4	no	—
64	C₄⋊C₈×C₁₃₇	—	2	4	no	—
65	C₄⋊C₈×C₁₃₇	—	2	2	no	—
66	#102×C₁₃₇	—	2	4	no	—
67	#102×C₁₃₇	—	2	4	no	—
68	#102×C₁₃₇	—	2	8	no	—
69	C₄×C₈×C₁₃₇	—	2	4	no	—
70	C₄×C₈×C₁₃₇	D₄	1	4	yes	—
71	#95×C₁₃₇	—	2	1	no	—
72	#95×C₁₃₇	—	2	1	no	—
73	#95×C₁₃₇	—	2	4	no	—
74	C₂⁴×C₁₃₇	—	2	2	no	—
75	C₂×Q₈×C₁₃₇	—	2	2	no	—
76	C₂×Q₈×C₁₃₇	—	2	2	no	—
77	C₂×Q₈×C₁₃₇	—	4	2	no	—
78	C₂×Q₈×C₁₃₇	—	8	2	no	—
79	C₂×Q₈×C₁₃₇	SD₁₆	1	4	yes	—
80	C₂×D₄×C₁₃₇	—	2	2	no	—
81	C₂×D₄×C₁₃₇	—	2	4	no	—
82	C₂×D₄×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	4	no	—
84	C₂×D₄×C₁₃₇	—	4	2	no	—
85	C₂×D₄×C₁₃₇	—	4	2	no	—
86	C₂×D₄×C₁₃₇	—	4	2	no	—
87	C₂×D₄×C₁₃₇	—	4	2	no	—
88	C₂×D₄×C₁₃₇	—	8	2	no	—
89	C₂²×C₄×C₁₃₇	—	2	2	no	—
90	C₂²×C₄×C₁₃₇	—	2	2	no	—
91	C₂²×C₄×C₁₃₇	—	2	2	no	—
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	2	no	—
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	—	2	4	no	—
101	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
103	C₄⋊C₄×C₁₃₇	—	2	4	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	2	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	4	2	no	—
111	C₄⋊C₄×C₁₃₇	—	8	4	no	—
112	C₄⋊C₄×C₁₃₇	#41	1	4	yes	—
113	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
114	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
115	C₄²×C₁₃₇	—	2	2	no	—
116	C₄²×C₁₃₇	—	2	2	no	—
117	C₄²×C₁₃₇	—	4	2	no	—
118	C₄²×C₁₃₇	—	4	2	no	—
119	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₄²×C₁₃₇	#41	1	2	yes	—
121	C₂³×C₁₃₇	—	4	2	no	—
122	C₂³×C₁₃₇	—	4	4	no	—
123	C₂³×C₁₃₇	—	4	2	no	—
124	C₂³×C₁₃₇	—	4	2	no	—
125	C₂³×C₁₃₇	—	4	4	no	—
126	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₁₃₇	—	2	8	no	—
128	Q₈×C₁₃₇	—	8	4	no	—
129	D₄×C₁₃₇	—	4	2	no	—
130	D₄×C₁₃₇	—	4	2	no	—
131	D₄×C₁₃₇	—	4	4	no	—
132	D₄×C₁₃₇	—	8	4	no	—
133	D₄×C₁₃₇	—	8	4	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	4	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	4	2	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	#121	1	2	yes	—
148	C₂×C₄×C₁₃₇	#121	1	2	yes	—
149	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
150	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₁₃₇	#135	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
156	C₈×C₁₃₇	—	2	2	no	—
157	C₈×C₁₃₇	—	2	2	no	—
158	C₈×C₁₃₇	—	4	2	no	—
159	C₂²×C₁₃₇	—	8	4	no	—
160	C₂²×C₁₃₇	—	8	4	no	—
161	C₂²×C₁₃₇	—	8	2	no	—
162	C₂²×C₁₃₇	—	8	2	no	—
163	C₂²×C₁₃₇	—	8	2	no	—
164	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
165	C₂²×C₁₃₇	#548	1	2	yes	—
166	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
167	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
168	C₂²×C₁₃₇	#576	1	2	yes	—
169	C₄×C₁₃₇	—	2	4	no	—
170	C₄×C₁₃₇	—	2	2	no	—
171	C₄×C₁₃₇	—	4	4	no	—
172	C₄×C₁₃₇	—	4	2	no	—
173	C₄×C₁₃₇	—	8	2	no	—
174	C₄×C₁₃₇	—	8	2	no	—
175	C₄×C₁₃₇	#465	1	4	yes	—
176	C₄×C₁₃₇	#532	1	1	yes	characteristic
177	C₄×C₁₃₇	#536	1	1	yes	characteristic
178	C₄×C₁₃₇	#556	1	2	yes	—
179	C₂×C₁₃₇	—	16	2	no	—
180	C₂×C₁₃₇	#2545	1	1	yes	characteristic
181	C₂×C₁₃₇	C₂×#465	1	1	yes	characteristic
182	C₂×C₁₃₇	#3058	1	1	yes	characteristic
183	C₂×C₁₃₇	#3361	1	2	yes	—
184	C₂×C₁₃₇	#3362	1	2	yes	—
185	#28640	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₇	#28640	1	1	yes	characteristic, direct product factor, Sylow
187	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
188	C₂×C₈×Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	#2567	C₂×C₁₃₇	1	1	yes	characteristic, complemented
190	#2548	C₂×C₁₃₇	1	1	yes	characteristic
191	#2065	C₂×C₁₃₇	1	4	yes	complemented
192	#1987	C₂×C₁₃₇	1	1	yes	characteristic, complemented
193	#1982	C₂×C₁₃₇	1	1	yes	characteristic
194	#1934	C₂×C₁₃₇	1	4	yes	complemented
195	C₄×#106	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
197	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
198	C₂×#124	—	2	1	no	—
199	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
200	#486	—	2	4	no	—
201	C₈×Q₈	—	2	4	no	—
202	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
206	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
207	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
210	#395	—	2	2	no	—
211	#394	—	2	2	no	—
212	#391	—	2	1	no	—
213	#390	—	2	1	no	—
214	#390	C₂²×C₁₃₇	1	4	yes	—
215	#389	C₂²×C₁₃₇	1	4	yes	—
216	#384	—	2	1	no	—
217	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
219	#340	C₂²×C₁₃₇	1	4	yes	—
220	#340	C₂²×C₁₃₇	1	2	yes	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
229	C₄⋊Q₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	#127	—	2	2	no	—
232	#127	—	2	2	no	—
233	#124	—	4	4	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
239	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
249	#106	—	2	4	no	—
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	2	no	—
252	#102	—	2	4	no	—
253	#102	—	2	4	no	—
254	#102	—	2	8	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	D₄×C₁₃₇	1	4	yes	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	#95	—	2	4	no	—
260	C₂⁴	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	8	2	no	—
265	C₂×Q₈	SD₁₆×C₁₃₇	1	4	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	8	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
288	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	8	4	no	—
298	C₄⋊C₄	#41×C₁₃₇	1	4	yes	—
299	C₂²⋊C₄	—	4	8	no	—
300	C₂²⋊C₄	—	8	4	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	2	no	—
304	C₄²	—	4	2	no	—
305	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
306	C₄²	#41×C₁₃₇	1	2	yes	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	2	no	—
311	C₂³	—	4	4	no	—
312	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
313	Q₈	—	2	8	no	—
314	Q₈	—	8	4	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	4	no	—
318	D₄	—	8	4	no	—
319	D₄	—	8	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	#121×C₁₃₇	1	2	yes	—
334	C₂×C₄	#121×C₁₃₇	1	2	yes	—
335	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
336	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
337	C₂×C₄	#135×C₁₃₇	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
340	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	4	no	—
349	C₂²	—	8	4	no	—
350	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
351	C₂²	#548×C₁₃₇	1	2	yes	—
352	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
353	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
354	C₂²	#576×C₁₃₇	1	2	yes	—
355	C₄	—	2	4	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	#465×C₁₃₇	1	4	yes	—
362	C₄	#532×C₁₃₇	1	1	yes	characteristic
363	C₄	#536×C₁₃₇	1	1	yes	characteristic
364	C₄	#556×C₁₃₇	1	2	yes	—
365	C₂	—	16	2	no	—
366	C₂	#2545×C₁₃₇	1	1	yes	characteristic
367	C₂	C₂×#465×C₁₃₇	1	1	yes	characteristic
368	C₂	#3058×C₁₃₇	1	1	yes	characteristic
369	C₂	#3361×C₁₃₇	1	2	yes	—
370	C₂	#3362×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄×Q₈×C₁₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₁₃₇	C₂	semidirect
3. #2567×C₁₃₇	C₂	semidirect
5. #2065×C₁₃₇	C₂	semidirect
6. #1987×C₁₃₇	C₂	semidirect
8. #1934×C₁₃₇	C₂	semidirect
9. C₄×#106×C₁₃₇	C₂	semidirect
185. #28640	C₁₃₇	direct (N × H)
186. C₁₃₇	#28640	direct (N × H)
188. C₂×C₈×Q₈	C₂×C₁₃₇	semidirect
189. #2567	C₂×C₁₃₇	semidirect
191. #2065	C₂×C₁₃₇	semidirect
192. #1987	C₂×C₁₃₇	semidirect
194. #1934	C₂×C₁₃₇	semidirect
195. C₄×#106	C₂×C₁₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#486×C₁₃₇	2
C₂×C₈×Q₈×C₁₃₇	2
#2567×C₁₃₇	2
#2548×C₁₃₇	2
#2065×C₁₃₇	2
#1987×C₁₃₇	2
#1982×C₁₃₇	2
#1934×C₁₃₇	2
C₄×#106×C₁₃₇	2
#28640	137

Subgroups — C137×#28640 #46878026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28640 #46878026